Existence and regularity of a nonhomogeneous transition matrix under measurability conditions
| dc.creator | Ye, Liuer | |
| dc.creator | Guo, Xianping | |
| dc.creator | Hernández-Lerma, Onésimo | |
| dc.date | 2008-04-28 | |
| dc.date.accessioned | 2026-07-07T09:35:38Z | |
| dc.date.available | 2026-07-07T09:35:38Z | |
| dc.description | This paper is about the existence and regularity of the transition probability matrix of a nonhomogeneous continuous-time Markov process with a countable state space. A standard approach to prove the existence of such a transition matrix is to begin with a continuous (in t) and conservative matrix Q(t)=[q_{ij}(t)] of nonhomogeneous transition rates q_{ij}(t), and use it to construct the transition probability matrix. Here we obtain the same result except that the q_{ij}(t) are only required to satisfy a mild measurability condition, and Q(t) may not be conservative. Moreover, the resulting transition matrix is shown to be the minimum transition matrix and, in addition, a necessary and sufficient condition for it to be regular is obtained. These results are crucial in some applications of nonhomogeneous continuous-time Markov processes, such as stochastic optimal control problems and stochastic games, which motivated this work in the first place. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/0804.4441 | |
| dc.identifier | http://arxiv.org/abs/0804.4441 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159897 | |
| dc.subject | Probability | |
| dc.subject | 60J27, 60J35, 60J75 | |
| dc.title | Existence and regularity of a nonhomogeneous transition matrix under measurability conditions | |
| dc.type | text |